A branch-and-bound algorithm for the exact optimal experimental design problem

Ahipaşaoğlu, Selin Damla

doi:10.1007/s11222-021-10043-5

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…It is challenging to analytically derive optimal designs for a given criterion under an arbitrary n and k. In practice, these criteria are optimized via some computer search algorithm, such as the coordinate exchange algorithm (Meyer and Nachtsheim, 1995), branch-andbound algorithms (Ahipaşaoglu, 2021), and nonlinear programming (Esteban-Bravo et al, 2017;Duarte et al, 2020). While the two latter algorithms offer some guarantees of identifying the true optimum, the coordinate exchange algorithm is straightforward to implement and is employed in popular statistical software.…”

Section: Properties Of the D-and A-criterionmentioning

confidence: 99%

D- and A-optimal Screening Designs

Stallrich¹,

Allen-Moyer²,

Jones³

2022

Preprint

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In practice, optimal screening designs for arbitrary run sizes are traditionally generated using the D-criterion with factor settings fixed at ±1, even when considering continuous factors with levels in [−1, 1]. This paper identifies cases of undesirable estimation variance properties for such D-optimal designs and argues that generally A-optimal designs tend to push variances closer to their minimum possible value. New insights about the behavior of the criteria are found through a study of their respective coordinateexchange formulas. The study confirms the existence of D-optimal designs comprised only of settings ±1 for both main effect and interaction models for blocked and unblocked experiments. Scenarios are also identified for which arbitrary manipulation of a coordinate between [−1, 1] leads to infinitely many D-optimal designs each having different variance properties. For the same conditions, the A-criterion is shown to have a unique optimal coordinate value for improvement. We also compare Bayesian version of the A-and D-criteria in how they balance minimization of estimation variance and bias. Multiple examples of screening designs are considered for various models under Bayesian and non-Bayesian versions of the A-and D-criteria.

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Section: Properties Of the D-and A-criterionmentioning

confidence: 99%

D- and A-optimal Screening Designs

Stallrich¹,

Allen-Moyer²,

Jones³

2022

Preprint

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The polytope of optimal approximate designs: extending the selection of informative experiments

Harman,

Filová,

Rosa

2024

Stat Comput

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Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution. Often, however, there exists a rich set of optimal designs, and the knowledge of this set can lead to substantially greater freedom to select an appropriate experiment. In this paper, we demonstrate that the set of all optimal approximate designs generally corresponds to a polytope. Particularly important elements of the polytope are its vertices, which we call vertex optimal designs. We prove that the vertex optimal designs possess unique properties, such as small supports, and outline strategies for how they can facilitate the construction of suitable experiments. Moreover, we show that for a variety of situations it is possible to construct the vertex optimal designs with the assistance of a computer, by employing error-free rational-arithmetic calculations. In such cases the vertex optimal designs are exact, often closely related to known combinatorial designs. Using this approach, we were able to determine the polytope of optimal designs for some of the most common multifactor regression models, thereby extending the choice of informative experiments for a large variety of applications.

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Mixed-integer linear programming for computing optimal experimental designs

Harman,

Rosa

2025

Journal of Statistical Planning and Inference

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A branch-and-bound algorithm for the exact optimal experimental design problem

Cited by 4 publications

References 39 publications

D- and A-optimal Screening Designs

D- and A-optimal Screening Designs

The polytope of optimal approximate designs: extending the selection of informative experiments

Mixed-integer linear programming for computing optimal experimental designs

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